LMFDB - Dirichlet character orbit 4020.dr

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(4020, base_ring=CyclotomicField(132)) M = H._module chi = DirichletCharacter(H, M([66,0,33,46])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(7,4020)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$4020$
Conductor:	$1340$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$132$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 1340.bv	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)

Related number fields

Field of values:	$\Q(\zeta_{132})$
Fixed field:	Number field defined by a degree 132 polynomial (not computed)

First 31 of 40 characters in Galois orbit

Character	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{4020}(7,\cdot)$	$-1$	$1$	$e\left(\frac{101}{132}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{49}{132}\right)$	$e\left(\frac{73}{132}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{1}{132}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{31}{66}\right)$
$\chi_{4020}(247,\cdot)$	$-1$	$1$	$e\left(\frac{113}{132}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{13}{132}\right)$	$e\left(\frac{49}{132}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{73}{132}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{19}{66}\right)$
$\chi_{4020}(367,\cdot)$	$-1$	$1$	$e\left(\frac{65}{132}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{25}{132}\right)$	$e\left(\frac{13}{132}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{49}{132}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{66}\right)$
$\chi_{4020}(463,\cdot)$	$-1$	$1$	$e\left(\frac{91}{132}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{35}{132}\right)$	$e\left(\frac{71}{132}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{95}{132}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{41}{66}\right)$
$\chi_{4020}(487,\cdot)$	$-1$	$1$	$e\left(\frac{37}{132}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{65}{132}\right)$	$e\left(\frac{113}{132}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{101}{132}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{29}{66}\right)$
$\chi_{4020}(547,\cdot)$	$-1$	$1$	$e\left(\frac{41}{132}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{97}{132}\right)$	$e\left(\frac{61}{132}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{37}{132}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{25}{66}\right)$
$\chi_{4020}(727,\cdot)$	$-1$	$1$	$e\left(\frac{109}{132}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{113}{132}\right)$	$e\left(\frac{101}{132}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{5}{132}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{23}{66}\right)$
$\chi_{4020}(787,\cdot)$	$-1$	$1$	$e\left(\frac{73}{132}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{89}{132}\right)$	$e\left(\frac{41}{132}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{53}{132}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{59}{66}\right)$
$\chi_{4020}(883,\cdot)$	$-1$	$1$	$e\left(\frac{71}{132}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{7}{132}\right)$	$e\left(\frac{67}{132}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{19}{132}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{61}{66}\right)$
$\chi_{4020}(1123,\cdot)$	$-1$	$1$	$e\left(\frac{19}{132}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{119}{132}\right)$	$e\left(\frac{83}{132}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{59}{132}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{47}{66}\right)$
$\chi_{4020}(1183,\cdot)$	$-1$	$1$	$e\left(\frac{67}{132}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{107}{132}\right)$	$e\left(\frac{119}{132}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{83}{132}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{65}{66}\right)$
$\chi_{4020}(1267,\cdot)$	$-1$	$1$	$e\left(\frac{25}{132}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{101}{132}\right)$	$e\left(\frac{5}{132}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{29}{132}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{41}{66}\right)$
$\chi_{4020}(1543,\cdot)$	$-1$	$1$	$e\left(\frac{79}{132}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{71}{132}\right)$	$e\left(\frac{95}{132}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{23}{132}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{53}{66}\right)$
$\chi_{4020}(1687,\cdot)$	$-1$	$1$	$e\left(\frac{5}{132}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{73}{132}\right)$	$e\left(\frac{1}{132}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{85}{132}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{61}{66}\right)$
$\chi_{4020}(1723,\cdot)$	$-1$	$1$	$e\left(\frac{31}{132}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{83}{132}\right)$	$e\left(\frac{59}{132}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{131}{132}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{35}{66}\right)$
$\chi_{4020}(1783,\cdot)$	$-1$	$1$	$e\left(\frac{95}{132}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{67}{132}\right)$	$e\left(\frac{19}{132}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{31}{132}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{37}{66}\right)$
$\chi_{4020}(1843,\cdot)$	$-1$	$1$	$e\left(\frac{119}{132}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{127}{132}\right)$	$e\left(\frac{103}{132}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{43}{132}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{13}{66}\right)$
$\chi_{4020}(1927,\cdot)$	$-1$	$1$	$e\left(\frac{85}{132}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{53}{132}\right)$	$e\left(\frac{17}{132}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{125}{132}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{47}{66}\right)$
$\chi_{4020}(1963,\cdot)$	$-1$	$1$	$e\left(\frac{23}{132}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{19}{132}\right)$	$e\left(\frac{31}{132}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{127}{132}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{43}{66}\right)$
$\chi_{4020}(1987,\cdot)$	$-1$	$1$	$e\left(\frac{1}{132}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{41}{132}\right)$	$e\left(\frac{53}{132}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{17}{132}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{65}{66}\right)$
$\chi_{4020}(2023,\cdot)$	$-1$	$1$	$e\left(\frac{115}{132}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{95}{132}\right)$	$e\left(\frac{23}{132}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{107}{132}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{17}{66}\right)$
$\chi_{4020}(2347,\cdot)$	$-1$	$1$	$e\left(\frac{13}{132}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{5}{132}\right)$	$e\left(\frac{29}{132}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{89}{132}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{53}{66}\right)$
$\chi_{4020}(2443,\cdot)$	$-1$	$1$	$e\left(\frac{83}{132}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{103}{132}\right)$	$e\left(\frac{43}{132}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{91}{132}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{49}{66}\right)$
$\chi_{4020}(2527,\cdot)$	$-1$	$1$	$e\left(\frac{97}{132}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{17}{132}\right)$	$e\left(\frac{125}{132}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{65}{132}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{35}{66}\right)$
$\chi_{4020}(2587,\cdot)$	$-1$	$1$	$e\left(\frac{29}{132}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{1}{132}\right)$	$e\left(\frac{85}{132}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{97}{132}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{37}{66}\right)$
$\chi_{4020}(2647,\cdot)$	$-1$	$1$	$e\left(\frac{53}{132}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{61}{132}\right)$	$e\left(\frac{37}{132}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{109}{132}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{13}{66}\right)$
$\chi_{4020}(2743,\cdot)$	$-1$	$1$	$e\left(\frac{59}{132}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{43}{132}\right)$	$e\left(\frac{91}{132}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{79}{132}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{66}\right)$
$\chi_{4020}(2767,\cdot)$	$-1$	$1$	$e\left(\frac{89}{132}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{85}{132}\right)$	$e\left(\frac{97}{132}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{61}{132}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{43}{66}\right)$
$\chi_{4020}(2827,\cdot)$	$-1$	$1$	$e\left(\frac{49}{132}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{29}{132}\right)$	$e\left(\frac{89}{132}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{41}{132}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{17}{66}\right)$
$\chi_{4020}(3043,\cdot)$	$-1$	$1$	$e\left(\frac{127}{132}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{59}{132}\right)$	$e\left(\frac{131}{132}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{47}{132}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{66}\right)$
$\chi_{4020}(3223,\cdot)$	$-1$	$1$	$e\left(\frac{35}{132}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{115}{132}\right)$	$e\left(\frac{7}{132}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{67}{132}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{31}{66}\right)$

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Character	\(-1\)	\(1\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{4020}(7,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{101}{132}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{49}{132}\right)\)	\(e\left(\frac{73}{132}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{1}{132}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{31}{66}\right)\)
\(\chi_{4020}(247,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{113}{132}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{13}{132}\right)\)	\(e\left(\frac{49}{132}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{73}{132}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{19}{66}\right)\)
\(\chi_{4020}(367,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{65}{132}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{25}{132}\right)\)	\(e\left(\frac{13}{132}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{49}{132}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{66}\right)\)
\(\chi_{4020}(463,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{91}{132}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{35}{132}\right)\)	\(e\left(\frac{71}{132}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{95}{132}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{41}{66}\right)\)
\(\chi_{4020}(487,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{37}{132}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{65}{132}\right)\)	\(e\left(\frac{113}{132}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{101}{132}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{29}{66}\right)\)
\(\chi_{4020}(547,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{41}{132}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{97}{132}\right)\)	\(e\left(\frac{61}{132}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{37}{132}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{25}{66}\right)\)
\(\chi_{4020}(727,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{109}{132}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{113}{132}\right)\)	\(e\left(\frac{101}{132}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{5}{132}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{23}{66}\right)\)
\(\chi_{4020}(787,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{73}{132}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{89}{132}\right)\)	\(e\left(\frac{41}{132}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{53}{132}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{59}{66}\right)\)
\(\chi_{4020}(883,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{71}{132}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{7}{132}\right)\)	\(e\left(\frac{67}{132}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{19}{132}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{61}{66}\right)\)
\(\chi_{4020}(1123,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{132}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{119}{132}\right)\)	\(e\left(\frac{83}{132}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{59}{132}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{47}{66}\right)\)
\(\chi_{4020}(1183,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{67}{132}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{107}{132}\right)\)	\(e\left(\frac{119}{132}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{83}{132}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{65}{66}\right)\)
\(\chi_{4020}(1267,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{25}{132}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{101}{132}\right)\)	\(e\left(\frac{5}{132}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{29}{132}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{41}{66}\right)\)
\(\chi_{4020}(1543,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{79}{132}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{71}{132}\right)\)	\(e\left(\frac{95}{132}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{23}{132}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{53}{66}\right)\)
\(\chi_{4020}(1687,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{132}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{73}{132}\right)\)	\(e\left(\frac{1}{132}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{85}{132}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{61}{66}\right)\)
\(\chi_{4020}(1723,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{132}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{83}{132}\right)\)	\(e\left(\frac{59}{132}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{131}{132}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{35}{66}\right)\)
\(\chi_{4020}(1783,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{95}{132}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{67}{132}\right)\)	\(e\left(\frac{19}{132}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{31}{132}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{37}{66}\right)\)
\(\chi_{4020}(1843,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{119}{132}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{127}{132}\right)\)	\(e\left(\frac{103}{132}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{43}{132}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{13}{66}\right)\)
\(\chi_{4020}(1927,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{85}{132}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{53}{132}\right)\)	\(e\left(\frac{17}{132}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{125}{132}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{47}{66}\right)\)
\(\chi_{4020}(1963,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{132}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{19}{132}\right)\)	\(e\left(\frac{31}{132}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{127}{132}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{43}{66}\right)\)
\(\chi_{4020}(1987,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{132}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{41}{132}\right)\)	\(e\left(\frac{53}{132}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{17}{132}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{65}{66}\right)\)
\(\chi_{4020}(2023,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{115}{132}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{95}{132}\right)\)	\(e\left(\frac{23}{132}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{107}{132}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{17}{66}\right)\)
\(\chi_{4020}(2347,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{132}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{5}{132}\right)\)	\(e\left(\frac{29}{132}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{89}{132}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{53}{66}\right)\)
\(\chi_{4020}(2443,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{83}{132}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{103}{132}\right)\)	\(e\left(\frac{43}{132}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{91}{132}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{49}{66}\right)\)
\(\chi_{4020}(2527,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{97}{132}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{17}{132}\right)\)	\(e\left(\frac{125}{132}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{65}{132}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{35}{66}\right)\)
\(\chi_{4020}(2587,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{132}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{1}{132}\right)\)	\(e\left(\frac{85}{132}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{97}{132}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{37}{66}\right)\)
\(\chi_{4020}(2647,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{53}{132}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{61}{132}\right)\)	\(e\left(\frac{37}{132}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{109}{132}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{13}{66}\right)\)
\(\chi_{4020}(2743,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{59}{132}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{43}{132}\right)\)	\(e\left(\frac{91}{132}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{79}{132}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{66}\right)\)
\(\chi_{4020}(2767,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{89}{132}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{85}{132}\right)\)	\(e\left(\frac{97}{132}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{61}{132}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{43}{66}\right)\)
\(\chi_{4020}(2827,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{49}{132}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{29}{132}\right)\)	\(e\left(\frac{89}{132}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{41}{132}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{17}{66}\right)\)
\(\chi_{4020}(3043,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{127}{132}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{59}{132}\right)\)	\(e\left(\frac{131}{132}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{47}{132}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{66}\right)\)
\(\chi_{4020}(3223,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{35}{132}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{115}{132}\right)\)	\(e\left(\frac{7}{132}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{67}{132}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{31}{66}\right)\)

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First 31 of 40 characters in Galois orbit

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	4020.dr
Modulus	$4020$
Conductor	$1340$
Order	$132$
Real	no
Primitive	no
Minimal	yes
Parity	odd

Modulus:	\(4020\)
Conductor:	\(1340\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(132\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 1340.bv	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)